In continuum elasticity, the displacement fields \(\vec{u} \equiv \delta \vec{r}\)  arising due to localised excess forces can be obtained using the well-known Lamé equation, which in two dimensions is [1]}
\(\mu \nabla ^2 \vec{u}(\vec{r}) + (\lambda + \mu ) \vec{\nabla }(\vec{\nabla } \cdot \vec{u}(\vec{r})) = -\vec{f}(\vec{r}),\) 
